Nuprl Lemma : int_formula_dnf_wf
∀[fmla:int_formula()]. (int_formula_dnf(fmla) ∈ polynomial-constraints() List)
Proof
Definitions occuring in Statement :
int_formula_dnf: int_formula_dnf(fmla),
polynomial-constraints: polynomial-constraints(),
int_formula: int_formula(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_formula_dnf: int_formula_dnf(fmla),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
polynomial-constraints: polynomial-constraints(),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
int_formula_ind_wf_simple,
list_wf,
polynomial-constraints_wf,
cons_wf,
nil_wf,
iPolynomial_wf,
int_term_to_ipoly_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
subtype_rel_product,
subtype_rel_list,
subtype_rel_self,
int_term_wf,
and-poly-constraints_wf,
int_formula_wf,
append_wf,
negate-poly-constraints_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
because_Cache,
independent_pairEquality,
voidEquality,
natural_numberEquality,
applyEquality,
independent_isectElimination,
voidElimination,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[fmla:int\_formula()]. (int\_formula\_dnf(fmla) \mmember{} polynomial-constraints() List)
Date html generated:
2016_05_14-AM-07_09_35
Last ObjectModification:
2015_12_26-PM-01_07_39
Theory : omega
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